The game of Matching Pennies (MP), a simplified version of the more popular Rock, Papers, Scissors, schematically represents competitions between organisms with incentives to predict each other's behavior. Optimal performance in iterated MP competitions involves the production of random choice patterns and the detection of nonrandomness in the opponent's choices. The purpose of this study was to replicate systematic deviations from optimal choice observed in humans when playing MP, and to establish whether suboptimal performance was better described by a modified linear learning model or by a more cognitively sophisticated reinforcement-tracking model. Two pairs of pigeons played iterated MP competitions; payoffs for successful choices (e.g., "Rock" vs. "Scissors") varied within experimental sessions and across experimental conditions, and were signaled by visual stimuli. Pigeons' behavior adjusted to payoff matrices; divergences from optimal play were analogous to those usually demonstrated by humans, except for the tendency of pigeons to persist on prior choices. Suboptimal play was well characterized by a linear learning model of the kind widely used to describe human performance. This linear learning model may thus serve as default account of competitive performance against which the imputation of cognitively sophisticated processes can be evaluated. (Contains 3 tables, 6 figures, and 2 footnotes.)